Can a carrier (heterozygote) of the wilson disease gene donate part of his/her liver tissue for a living related donor transplant to a patient?

Yes: The answer will generally be yes and the liver will not be affected by wilson's disease but the identified donor will undergo a full battery of tests to ensure safety for surgery. The interests of the donor are always of the highest concern.

Yes: Wilsons disease is a disease of copper storage. It is genetically linked. Generally speaking people who are heterozygous (are only carriers) can donate their part of thier livers. People who are heterozygous are carriers and don't have wilson's disease themselves.